On the Diophantine Equation 1K + 2K + ... + Xk + R(X) = Yz

摘要

The following theorem is proven: let R(x) be a fixed polynomial with rational integer coefficients; let b not = o and k or = 2 be fixed rational integers such that k does not belong to the interval (3,5); then the equation 1k + 2k + ... + xk + R (x) = byz in integers x, y, or = to 1 and 2 1 has only finitely many solutions.